Can high-angle annular dark field scattering be represented by a local operator?

Area of Science:

• Materials Science
• Electron Microscopy
• Solid-State Physics

Background:

• High-angle annular dark field (HAADF) imaging is a key technique for achieving atomic resolution in scanning transmission electron microscopy (STEM).
• Current analysis methods often simplify HAADF signals as a local scattering process, assuming a convolution of the probe with atomic columns.
• This simplification has led to the belief that impurity concentrations can be quantified at atomic resolution due to signal dependence on atomic number.

Purpose of the Study:

• To examine the limitations of the local scattering operator approximation in HAADF imaging.
• To investigate the validity of quantifying impurity concentrations at atomic resolution using HAADF.
• To explore the influence of multi-phonon excitations on high-angle scattering in STEM.

Main Methods:

• Developed a complete theory for high-angle scattering, incorporating multi-phonon excitations.
• Analyzed approximations based on this complete theory to assess the local scattering operator model.
• Investigated the relationship between inner cut-off angles and the accuracy of the scattering approximation.

Main Results:

• The study identifies limitations in the assumption of a simple local scattering operator for HAADF signal analysis.
• The accuracy of the local scattering operator approximation is shown to be dependent on the chosen inner cut-off angle.
• Increased inner cut-off angles lead to improved accuracy of the local scattering approximation in HAADF imaging.

Conclusions:

• The apparent simplicity of HAADF imaging can mask underlying complexities in signal interpretation.
• Quantifying impurity concentrations at atomic resolution requires careful consideration of scattering physics beyond the local approximation.
• Optimizing the inner cut-off angle is critical for enhancing the reliability of quantitative HAADF STEM analysis.